Public Opinion Statistics Benchmark
Recent polling reveals that 1 in 10 French adults (10%) believe their country is headed in the "right track". Explore how sample size ($N$), confidence levels, and binomial sampling variance affect the accuracy of public sentiment polling.
Poll Parameters
1,000
N=100
N=2,500
N=5,000
N=10,000
10.0%
1%
10% (Baseline)
25%
50%
1,000 polls
Standard Error ($SE$)
0.00948
$\sqrt{p(1-p)/N}$
Margin of Error
±1.86%
at 95% Confidence
Wilson 95% Lower
8.22%
Score Interval Limit
Wilson 95% Upper
12.06%
Score Interval Limit
Empirical Sampling Distribution vs Wilson Bounds
D3.js Live Chart
Poll Outcomes
Normal Curve
Wilson Bounds
A sample size of 1,000 adults with p=0.10 yields a 95% confidence interval of [8.22%, 12.06%] with a margin of error of ±1.86%.
Sample Size ($N$) vs. Margin of Error Curve
Diminishing returns of increasing poll sample size at $p = 10\%$
Notice how expanding the sample size from N=100 to N=1,000 slashes the margin of error dramatically from ±5.88% to ±1.86%, whereas boosting from N=1,000 to N=10,000 yields only a modest further reduction to ±0.59%.
Demographic Cross-Section Matrix
Stratified weighted sentiment impact across French demographic sub-groups
Stratified vs Unstratified Sampling SE Delta:
-0.0012 SE Reduction
Historical French Public Sentiment Polling Reference Benchmarks
Comparative sensitivity across sample sizes for low-proportion sentiment statistics